Analytical model to predict unfrozen water content based on the probability of ice formation in soils

The variation in unfrozen water content with temperature substantially affects coupled heat and water transport in frozen soil, causing frost heave and thaw settlement owing to the ice and water phase change and influencing soil stability in cold regions. Thus, analyzing the mechanism of water freezing and building a predictive model for the unfrozen water content of soils is paramount. In this study, an analytical model based on equivalent contact angle was developed to predict the unfrozen water content. The relationship between the equivalent contact angle and temperature was obtained based on the assumption that the heterogeneous nucleation rate nonlinearly decreased with temperature. The proposed analytical model was validated using existing unfrozen water content data at various temperatures for a silty clay soil material from the Qinghai-Tibet Plateau, and compared to several existing numerical models which predict unfrozen water content in soil materials. The results revealed a close relationship between the unfrozen water content and equivalent contact angle, and the equivalent contact angle increased as the temperature decreased. Meanwhile, the pore water in the soil first froze when the contact angle was smaller. Moreover, the values predicted by the analytical model for the unfrozen water content agreed well with the experimental results, especially under low-temperature conditions and during the early stage of water freezing.